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Simplifying 4.9t2 + 8t + -550 = 0 Reorder the terms: -550 + 8t + 4.9t2 = 0 Solving -550 + 8t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -112.244898 + 1.632653061t + t2 = 0 Move the constant term to the right: Add '112.244898' to each side of the equation. -112.244898 + 1.632653061t + 112.244898 + t2 = 0 + 112.244898 Reorder the terms: -112.244898 + 112.244898 + 1.632653061t + t2 = 0 + 112.244898 Combine like terms: -112.244898 + 112.244898 = 0.000000 0.000000 + 1.632653061t + t2 = 0 + 112.244898 1.632653061t + t2 = 0 + 112.244898 Combine like terms: 0 + 112.244898 = 112.244898 1.632653061t + t2 = 112.244898 The t term is 1.632653061t. Take half its coefficient (0.8163265305). Square it (0.6663890044) and add it to both sides. Add '0.6663890044' to each side of the equation. 1.632653061t + 0.6663890044 + t2 = 112.244898 + 0.6663890044 Reorder the terms: 0.6663890044 + 1.632653061t + t2 = 112.244898 + 0.6663890044 Combine like terms: 112.244898 + 0.6663890044 = 112.9112870044 0.6663890044 + 1.632653061t + t2 = 112.9112870044 Factor a perfect square on the left side: (t + 0.8163265305)(t + 0.8163265305) = 112.9112870044 Calculate the square root of the right side: 10.625972285 Break this problem into two subproblems by setting (t + 0.8163265305) equal to 10.625972285 and -10.625972285.Subproblem 1
t + 0.8163265305 = 10.625972285 Simplifying t + 0.8163265305 = 10.625972285 Reorder the terms: 0.8163265305 + t = 10.625972285 Solving 0.8163265305 + t = 10.625972285 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8163265305' to each side of the equation. 0.8163265305 + -0.8163265305 + t = 10.625972285 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + t = 10.625972285 + -0.8163265305 t = 10.625972285 + -0.8163265305 Combine like terms: 10.625972285 + -0.8163265305 = 9.8096457545 t = 9.8096457545 Simplifying t = 9.8096457545Subproblem 2
t + 0.8163265305 = -10.625972285 Simplifying t + 0.8163265305 = -10.625972285 Reorder the terms: 0.8163265305 + t = -10.625972285 Solving 0.8163265305 + t = -10.625972285 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8163265305' to each side of the equation. 0.8163265305 + -0.8163265305 + t = -10.625972285 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + t = -10.625972285 + -0.8163265305 t = -10.625972285 + -0.8163265305 Combine like terms: -10.625972285 + -0.8163265305 = -11.4422988155 t = -11.4422988155 Simplifying t = -11.4422988155Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.8096457545, -11.4422988155}
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